Question

How do you write `y=x^2+7x-1` in vertex form?

Answer 1

`y = (x + 7/2)^2 - 53/4`

Explanation:

x-coordinate of vertex:
`x = -b/(2a) = -7/2`
y-coordinate of vertex (when `x = -7/2`):
`y(-7/2) = 49/4 - 7(7/2) - 1 = 49/4 - 49/2 - 1 = -53/4`
Vertex `(-7/2, -53/4)`
Vertex form of y:
`y = a(x + b/(2a)) + y(-b/(2a))`
`y = (x + 7/2)^2 - 53/4`